where \(\gamma \)  is the surface tension, \(\kappa \)  is the signed curvature of \(\partial \Omega \) , defined to be positive if the interface is convex from the fluid side, and \(v_n\)  is the normal speed of the interface. Typically the flow is driven by injection or withdrawal of fluid through a point or at infinity. This original model for two immiscible fluids is described by Saffman & Taylor [1]} in 1958, except that for the most part they kept track of both fluids.
